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It states that any equation describing a physical situation carries equivalent units on either side of the equals sign.
An example of an equation which falls under this category is Newton's second law: F = ma, where F describes a force in Newtons, m a mass in kilograms and a an acceleration in meters/second^2. By definition (and by application of this law), a Newton is equivalent to a kg*m/s^2.
Another is a quantity of kinetic energy: E = (1/2)mv^2. E is an energy dimension (let's use Joules as our units), mass can be given in kg and velocity in meters/second. The right hand side therefore carries units of kg*m^2/s^2. Regrouping these gives us (kg*m/s^2) * m. You may recognize the bracketed term from the paragraph above: it is equivalent to a dimension of force, the Newton. We can express this as N*m, which, (when they act in parallel, and they do here) is the definition of a Joule, so dimensions on either side are equivalent.
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JordanDimensional homogeneity refers to the concept that the units on the left-hand side of an equation must be equivalent to the units on the right-hand side for the equation to be mathematically valid. It is widely used in physics and engineering to ensure that equations accurately represent physical relationships and can be used consistently in calculations without errors due to mismatched units.
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Examples: chemical reactivity, flammability, solubility, chemical composition, homogeneity or heterogeneity, toxicity.
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